Hi,
Well, I have a hint which can help. There is a new bound for the number of the
Mistakes the Perceptron algorithm makes. In terms of SVM the bound is
proportional to (for all w)
(1/2)||w||^2 R^2 + \sum_i \max\{0, 1-y_i(w*x_i)\}
where it is assumed that all the examples are in a ball of radius R around the
origin.
If you take the factor R^2 out of the bound you get the SVM optimization
problem, where C=1/R^2 ; a max operator is used rather than the mean operator
you asked about. I am not sure if the bound still holds if we replace the
max with a mean. In practice, the mean is more stable than the max. (Although I would try to use
also the median).
Regards, Koby
============================================
Koby Crammer [log in to unmask]
http://www.cs.huji.ac.il/~kobics
============================================
On Thu, 27 May 2004, Dave Lewis wrote:
| Hi - SVM Light has as the default value of its regularization parameter
| (tradeoff between training error and margin) the reciprocal of the mean
| 2-norm of the training examples. Does anyone know what the statistical
| justification for this particular choice is? I can't seem to find this in
| Thorsten Joachim's papers.
|
| Regards, Dave
| http://www.DavidDLewis.com
|
